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nuckollsr(at)cox.net
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 Posted: Wed Apr 12, 2006 9:57 am Post subject: More Old Struff |
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| Quote: |
Pretty soon I am going to introduce the concept of lines of position
(LOPs) and how pilotage, VOR, GPS, and celestial navigation work. No,
they are not going to become navigators but they sure as heck will know
that mathematics is both useful and fun.
|
LOPs are pretty cool. Received an introduction to the concept
at astrocompass school at Boeing many moons ago. It was easy
to visualize that any give star has an infinite number of
locations on the earth where it appears x-degrees above the
horizon. So, shooting one star and knowing time of day to
access the almanac, you could deduce an infinite number of
accurate possibilities as to where you were. Shoot a second
star and intersections reduce infinite to two, shoot a third
and you're down to one possible location.
When I studied LORAN years later and taught it at Great Lakes,
LOP's plotted with timing of shore based radio signals vs.
angles above horizon proved just as useful.
Nowadays, GPS does exactly the same thing except timing
comes off of stations whizzing above the earth.
Bob . . .
< What is so wonderful about scientific truth...is that >
< the authority which determines whether there can be >
< debate or not does not reside in some fraternity of >
< scientists; nor is it divine. The authority rests >
< with experiment. >
< --Lawrence M. Krauss >
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brian
Joined: 02 Jan 2006
Posts: 643
Location: Sacramento, California, USA
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| Posted: Wed Apr 12, 2006 10:40 am Post subject: More Old Struff |
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Robert L. Nuckolls, III wrote:
| Quote: | LOPs are pretty cool. Received an introduction to the concept
at astrocompass school at Boeing many moons ago. It was easy
to visualize that any give star has an infinite number of
locations on the earth where it appears x-degrees above the
horizon.
|
Right. It is a circle centered on the point on the earth where the
object is at the zenith (declination is 90 degrees). The distance from
that point is the sin of the elevation times 1/4 the circumference of
the earth.
| Quote: | So, shooting one star and knowing time of day to
access the almanac, you could deduce an infinite number of
accurate possibilities as to where you were.
|
Right, a *line* of position.
| Quote: | Shoot a second
star and intersections reduce infinite to two, shoot a third
and you're down to one possible location.
When I studied LORAN years later and taught it at Great Lakes,
LOP's plotted with timing of shore based radio signals vs.
angles above horizon proved just as useful.
|
Right, and you can cross LOPs from anything to find your position. You
can cross a LORAN TD LOP with a celestial LOP to get a position. It is
very cool stuff.
I plan to introduce the concept to the kids by using a road as one LOP
and a compass bearing off a landmark as another. It is something they
can get their hands around right away. From there I will introduce more
esoteric stuff like two bearings (triangulation) and then on to other
stuff if they can handle it.
| Quote: |
Nowadays, GPS does exactly the same thing except timing
comes off of stations whizzing above the earth.
|
A little different. Celestial is based on angles which define a circle
on the surface of the earth. GPS "LOPs" are actually spheres defined by
a time (distance) from the satellite. One bird defines a sphere. Two
define a circle. Three define two intersecting circles or two points.
Four defines a single point which is why you need to see four satellites
in order to have three-D navigation. Many GPS receivers use the altitude
encoder to define a pseudo-range from the center of the earth to
simulate another satellite. It is just another form of LOP.
I love this stuff.
--
Brian Lloyd 361 Catterline Way
brian-yak at lloyd dot com Folsom, CA 95630
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery
| | - The Matronics AeroElectric-List Email Forum - | | | Use the List Feature Navigator to browse the many List utilities available such as the Email Subscriptions page, Archive Search & Download, 7-Day Browse, Chat, FAQ, Photoshare, and much more:
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_________________
Brian Lloyd
brian-yak at lloyd dot com
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery |
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mprather(at)spro.net
Guest
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| Posted: Wed Apr 12, 2006 10:54 am Post subject: More Old Struff |
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I like the astro-inertial concept, as used on various craft. Forget
jammed GPS. Just have to fly above the clouds. Works in daylight too.
http://www.dtic.mil/matris/sbir/sbir021/n104.pdf
What is old is new..
Matt-
| Quote: |
<nuckollsr(at)cox.net>
>
>
>Pretty soon I am going to introduce the concept of lines of position
> (LOPs) and how pilotage, VOR, GPS, and celestial navigation work. No,
> they are not going to become navigators but they sure as heck will know
> that mathematics is both useful and fun.
LOPs are pretty cool. Received an introduction to the concept
at astrocompass school at Boeing many moons ago. It was easy
to visualize that any give star has an infinite number of
locations on the earth where it appears x-degrees above the
horizon. So, shooting one star and knowing time of day to
access the almanac, you could deduce an infinite number of
accurate possibilities as to where you were. Shoot a second
star and intersections reduce infinite to two, shoot a third
and you're down to one possible location.
When I studied LORAN years later and taught it at Great Lakes, LOP's
plotted with timing of shore based radio signals vs.
angles above horizon proved just as useful.
Nowadays, GPS does exactly the same thing except timing
comes off of stations whizzing above the earth.
Bob . . .
< What is so wonderful about scientific truth...is that >
< the authority which determines whether there can be >
< debate or not does not reside in some fraternity of >
< scientists; nor is it divine. The authority rests >
< with experiment. >
< --Lawrence M. Krauss >
|
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khorton01(at)rogers.com
Guest
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| Posted: Wed Apr 12, 2006 2:25 pm Post subject: More Old Struff |
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On 12 Apr 2006, at 14:39, Brian Lloyd wrote:
| Quote: |
yak(at)lloyd.com>
A little different. Celestial is based on angles which define a circle
on the surface of the earth. GPS "LOPs" are actually spheres
defined by
a time (distance) from the satellite. One bird defines a sphere. Two
define a circle. Three define two intersecting circles or two points.
Four defines a single point which is why you need to see four
satellites
in order to have three-D navigation. Many GPS receivers use the
altitude
encoder to define a pseudo-range from the center of the earth to
simulate another satellite. It is just another form of LOP.
|
I thought we needed the fourth satellite to correct for inaccuracy in
the GPS receiver's clock.
Three satellites would be enough, if the receiver had an extremely
accurate clock, and you make the assumption that the receiver is
somewhere close to the earth's surface. As you say, if you have
three satellites, that will give two possible points, but one of
those points is way, way out in space, and you can assume that this
point is not the right one. The info from the fourth satellite is
used to determine the error in the receiver's clock. The clock needs
to be correct with nanosecond accuracy to resolve ranges to a few
feet. The satellites have extremely accurate, very, very expensive
clocks to sync the signals to. But the receivers only have cheap,
much less accurate clocks. The lines of position from the fourth
satellite don't agree with the ones from the others if there is an
error in the receiver's clock. The assumed clock error is adjusted
until the info from all satellites agrees.
Kevin Horton RV-8 (finishing kit)
Ottawa, Canada
http://www.kilohotel.com/rv8
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brian
Joined: 02 Jan 2006
Posts: 643
Location: Sacramento, California, USA
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| Posted: Wed Apr 12, 2006 5:47 pm Post subject: More Old Struff |
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Matt Prather wrote:
Oh, this is very cool. I want one in my plane. No one can jam it or turn
it off.
--
Brian Lloyd 361 Catterline Way
brian-yak at lloyd dot com Folsom, CA 95630
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery
| | - The Matronics AeroElectric-List Email Forum - | | | Use the List Feature Navigator to browse the many List utilities available such as the Email Subscriptions page, Archive Search & Download, 7-Day Browse, Chat, FAQ, Photoshare, and much more:
http://www.matronics.com/Navigator?AeroElectric-List |
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_________________
Brian Lloyd
brian-yak at lloyd dot com
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery |
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brian
Joined: 02 Jan 2006
Posts: 643
Location: Sacramento, California, USA
|
| Posted: Wed Apr 12, 2006 5:55 pm Post subject: More Old Struff |
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Kevin Horton wrote:
| Quote: | I thought we needed the fourth satellite to correct for inaccuracy in
the GPS receiver's clock.
|
That is probably right although most GPS sensors will do 2D nav with
just three satellites and assume surface of the earth to resolve the errors.
--
Brian Lloyd 361 Catterline Way
brian-yak at lloyd dot com Folsom, CA 95630
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery
| | - The Matronics AeroElectric-List Email Forum - | | | Use the List Feature Navigator to browse the many List utilities available such as the Email Subscriptions page, Archive Search & Download, 7-Day Browse, Chat, FAQ, Photoshare, and much more:
http://www.matronics.com/Navigator?AeroElectric-List |
|
_________________
Brian Lloyd
brian-yak at lloyd dot com
+1.916.367.2131 (voice) +1.270.912.0788 (fax)
I fly because it releases my mind from the tyranny of petty things . . .
- Antoine de Saint-Exupery |
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rv8ch
Joined: 10 Jan 2006
Posts: 250
Location: Switzerland
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brian
Joined: 02 Jan 2006
Posts: 643
Location: Sacramento, California, USA
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